tdehaeze/nass-micro-station-measurements
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Add analysis about simultaneous rotation and translation

Browse Source
This commit is contained in:
Thomas Dehaeze
2019-05-15 15:49:48 +02:00
parent dd484e8a3b
commit df4d100ddf
25 changed files with 1054 additions and 141 deletions
Download Patch File Download Diff File Expand all files Collapse all files

BIN
disturbance-ty-sr/figs/current_time.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 48 KiB

BIN
disturbance-ty-sr/figs/psd_marble_compare.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 179 KiB

BIN
disturbance-ty-sr/figs/psd_relative_compare.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 195 KiB

BIN
disturbance-ty-sr/figs/psd_sample_compare.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 178 KiB

BIN
disturbance-ty-sr/figs/ty_current_time.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 71 KiB

BIN
disturbance-ty-sr/figs/ty_marble_time.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 72 KiB

BIN
disturbance-ty-sr/figs/ty_marble_time_zoom.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 74 KiB

BIN
disturbance-ty-sr/figs/ty_position_time.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 76 KiB

BIN
disturbance-ty-sr/figs/ty_relative_disp_time.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 65 KiB

BIN
disturbance-ty-sr/figs/ty_relative_time.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 77 KiB

BIN
disturbance-ty-sr/figs/ty_relative_time_zoom.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 80 KiB

BIN
disturbance-ty-sr/figs/ty_sample_time.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 76 KiB

BIN
disturbance-ty-sr/figs/ty_sample_time_zoom.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 86 KiB

391
disturbance-ty-sr/index.html
View File

@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-05-15 mer. 08:38 -->
<!-- 2019-05-15 mer. 15:49 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by simultaneous scans of the translation stage and of the slip-ring</title>
@@ -258,19 +258,28 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org8a17ec6">1. Measurement description</a></li>
<li><a href="#orgf15470a">2. Data Analysis</a>
<li><a href="#orge303e87">1. Measurement description</a></li>
<li><a href="#orgc23d6dc">2. Data Analysis</a>
<ul>
<li><a href="#org2066778">2.1. Load data</a></li>
<li><a href="#org5bdcb1d">2.2. Time domain plots</a></li>
<li><a href="#org629d4b4">2.1. Load data</a></li>
<li><a href="#org79a2c27">2.2. Voltage to Velocity</a></li>
<li><a href="#org1bafa09">2.3. Time domain plots</a></li>
<li><a href="#org05973bc">2.4. Frequency Domain</a></li>
<li><a href="#org57188a5">2.5. Ty motion and current</a>
<ul>
<li><a href="#org07bb77c">2.5.1. Data pre-processing</a></li>
<li><a href="#org8bcb0f7">2.5.2. Time domain data</a></li>
</ul>
</li>
<li><a href="#org005d22e">2.6. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org8a17ec6" class="outline-2">
<h2 id="org8a17ec6"><span class="section-number-2">1</span> Measurement description</h2>
<div id="outline-container-orge303e87" class="outline-2">
<h2 id="orge303e87"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1">
<p>
<b>Setup</b>:
@@ -375,11 +384,11 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div>
</div>
<div id="outline-container-orgf15470a" class="outline-2">
<h2 id="orgf15470a"><span class="section-number-2">2</span> Data Analysis</h2>
<div id="outline-container-orgc23d6dc" class="outline-2">
<h2 id="orgc23d6dc"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orgd07fa1b"></a>
<a id="org4563c51"></a>
</p>
<div class="note">
<p>
@@ -389,63 +398,377 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div>
</div>
<div id="outline-container-org2066778" class="outline-3">
<h3 id="org2066778"><span class="section-number-3">2.1</span> Load data</h3>
<div id="outline-container-org629d4b4" class="outline-3">
<h3 id="org629d4b4"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">ty_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_050.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_off = ty_off.data;
ty_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_on = ty_on.data;
ty_1hz = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_052.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_1hz = ty_1hz.data;
<pre class="src src-matlab">ty_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_050.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_of = ty_of.data;
ty_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_on = ty_on.data;
ty_1h = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_052.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_1h = ty_1h.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org5bdcb1d" class="outline-3">
<h3 id="org5bdcb1d"><span class="section-number-3">2.2</span> Time domain plots</h3>
<div id="outline-container-org79a2c27" class="outline-3">
<h3 id="org79a2c27"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/MEGA/These/meas/src/index.html">here</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">40</span>; <span class="org-comment">% [dB]</span>
ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
ty_on<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
ty_1h<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
ty_on<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
ty_1h<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org1bafa09" class="outline-3">
<h3 id="org1bafa09"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We plot the measured velocity of the marble (figure <a href="#org53f1c30">1</a>), sample (figure <a href="#org6938117">2</a>) and the relative velocity of the sample with respect to the marble (figure <a href="#orgfd8af3e">3</a>).
</p>
<p>
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#org425e005">4</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1hz<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1hz<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
<div id="org53f1c30" class="figure">
<p><img src="figs/ty_marble_time.png" alt="ty_marble_time.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Velocity of the marble in the vertical direction</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1hz<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1hz<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org6938117" class="figure">
<p><img src="figs/ty_sample_time.png" alt="ty_sample_time.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Velocity of the sample in the vertical direction</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative Velocity <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Velocity - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Velocity - Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgfd8af3e" class="figure">
<p><img src="figs/ty_relative_time.png" alt="ty_relative_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Relative velocity of the sample with respect to the marble</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative Displacement<span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Displacement- Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Displacement- Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Displacement </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org425e005" class="figure">
<p><img src="figs/ty_relative_disp_time.png" alt="ty_relative_disp_time.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Relative Displacement of the sample with respect to the marble</p>
</div>
</div>
</div>
<div id="outline-container-org05973bc" class="outline-3">
<h3 id="org05973bc"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<p>
First for the geophone located on the marble
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And for the geophone located at the sample position.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Finally, for the relative velocity.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And we plot the ASD of the measured velocities:
</p>
<ul class="org-ul">
<li>figure <a href="#org00eb9e9">5</a> for the geophone located on the marble</li>
<li>figure <a href="#org192c441">6</a> for the geophone at the sample position</li>
<li>figure <a href="#org1b88cd2">7</a> for the relative velocity</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org00eb9e9" class="figure">
<p><img src="figs/psd_marble_compare.png" alt="psd_marble_compare.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org192c441" class="figure">
<p><img src="figs/psd_sample_compare.png" alt="psd_sample_compare.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org1b88cd2" class="figure">
<p><img src="figs/psd_relative_compare.png" alt="psd_relative_compare.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Comparison of the ASD of the relative velocity</p>
</div>
</div>
</div>
<div id="outline-container-org57188a5" class="outline-3">
<h3 id="org57188a5"><span class="section-number-3">2.5</span> Ty motion and current</h3>
<div class="outline-text-3" id="text-2-5">
<p>
The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
</p>
</div>
<div id="outline-container-org07bb77c" class="outline-4">
<h4 id="org07bb77c"><span class="section-number-4">2.5.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-5-1">
<p>
Let's look at at the start of the csv file.
</p>
<div class="org-src-container">
<pre class="src src-bash">sed -n <span class="org-highlight-numbers-number">1,30p</span> mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
</pre>
</div>
<p>
The real data starts at line 29.
We then load this <code>cvs</code> file starting at line 29.
</p>
<div class="org-src-container">
<pre class="src src-matlab">tye_on = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
tye_1h = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span><span class="org-type">-</span>and<span class="org-type">-</span>Ty<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org8bcb0f7" class="outline-4">
<h4 id="org8bcb0f7"><span class="section-number-4">2.5.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-5-2">
<p>
We plot the position of the translation stage measured by the encoders.
</p>
<p>
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
</p>
<p>
The result is shown on figure <a href="#orgfeb408e">8</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">(</span>tye_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_on<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">(</span>tye_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_1h<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgfeb408e" class="figure">
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Y position of the translation stage measured by the encoders</p>
</div>
<p>
We also plot the current as function of the time on figure <a href="#orgbd294dc">9</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgbd294dc" class="figure">
<p><img src="figs/ty_current_time.png" alt="ty_current_time.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Current going through the actuator of the translation stage</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org005d22e" class="outline-3">
<h3 id="org005d22e"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<ul class="org-ul">
<li></li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-15 mer. 08:38</p>
<p class="date">Created: 2019-05-15 mer. 15:49</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

362
disturbance-ty-sr/index.org
View File

@@ -93,6 +93,7 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
addpath('../src');
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
@@ -101,40 +102,351 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
** Load data
#+begin_src matlab
ty_off = load('mat/data_050.mat', 'data'); ty_off = ty_off.data;
ty_on = load('mat/data_051.mat', 'data'); ty_on = ty_on.data;
ty_1hz = load('mat/data_052.mat', 'data'); ty_1hz = ty_1hz.data;
ty_of = load('mat/data_050.mat', 'data'); ty_of = ty_of.data;
ty_on = load('mat/data_051.mat', 'data'); ty_on = ty_on.data;
ty_1h = load('mat/data_052.mat', 'data'); ty_1h = ty_1h.data;
#+end_src
** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
#+begin_src matlab
gain = 40; % [dB]
ty_of(:, 1) = voltageToVelocityL22(ty_of(:, 1), ty_of(:, 3), gain);
ty_on(:, 1) = voltageToVelocityL22(ty_on(:, 1), ty_on(:, 3), gain);
ty_1h(:, 1) = voltageToVelocityL22(ty_1h(:, 1), ty_1h(:, 3), gain);
ty_of(:, 2) = voltageToVelocityL22(ty_of(:, 2), ty_of(:, 3), gain);
ty_on(:, 2) = voltageToVelocityL22(ty_on(:, 2), ty_on(:, 3), gain);
ty_1h(:, 2) = voltageToVelocityL22(ty_1h(:, 2), ty_1h(:, 3), gain);
#+end_src
** Time domain plots
#+begin_src matlab
figure;
hold on;
plot(ty_1hz(:, 3), ty_1hz(:, 1), 'DisplayName', 'Marble - Z');
plot(ty_on(:, 3), ty_on(:, 1), 'DisplayName', 'Marble - Z');
plot(ty_off(:, 3), ty_off(:, 1), 'DisplayName', 'Marble - Z');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-5, 5]);
legend('Location', 'northeast');
#+end_src
We plot the measured velocity of the marble (figure [[fig:ty_marble_time]]), sample (figure [[fig:ty_sample_time]]) and the relative velocity of the sample with respect to the marble (figure [[fig:ty_relative_time]]).
#+begin_src matlab
xlim([0, 1]);
#+end_src
We also integrate the relative velocity to obtain the relative displacement (figure [[fig:ty_relative_disp_time]]).
#+begin_src matlab
figure;
hold on;
plot(ty_1hz(:, 3), ty_1hz(:, 2), 'DisplayName', 'Marble - Z');
plot(ty_on(:, 3), ty_on(:, 2), 'DisplayName', 'Marble - Z');
plot(ty_off(:, 3), ty_off(:, 2), 'DisplayName', 'Marble - Z');
plot(ty_1h(:, 3), ty_1h(:, 1), 'DisplayName', 'Marble - Ty 1Hz');
plot(ty_on(:, 3), ty_on(:, 1), 'DisplayName', 'Marble - Ty ON');
plot(ty_of(:, 3), ty_of(:, 1), 'DisplayName', 'Marble - Ty OFF');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-5, 5]);
legend('Location', 'northeast');
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 2]);
legend('Location', 'southwest');
#+end_src
#+begin_src matlab
xlim([0, 1]);
#+NAME: fig:ty_marble_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_marble_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_marble_time
#+CAPTION: Velocity of the marble in the vertical direction
#+RESULTS: fig:ty_marble_time
[[file:figs/ty_marble_time.png]]
#+begin_src matlab
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2), 'DisplayName', 'Sample - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2), 'DisplayName', 'Sample - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2), 'DisplayName', 'Sample - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 2]);
legend('Location', 'southwest');
#+end_src
#+NAME: fig:ty_sample_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_sample_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_sample_time
#+CAPTION: Velocity of the sample in the vertical direction
#+RESULTS: fig:ty_sample_time
[[file:figs/ty_sample_time.png]]
#+begin_src matlab
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2)-ty_1h(:, 1), 'DisplayName', 'Relative Velocity - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2)-ty_on(:, 1), 'DisplayName', 'Relative Velocity - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2)-ty_of(:, 1), 'DisplayName', 'Relative Velocity - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 2]);
legend('Location', 'southwest');
#+end_src
#+NAME: fig:ty_relative_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_relative_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_relative_time
#+CAPTION: Relative velocity of the sample with respect to the marble
#+RESULTS: fig:ty_relative_time
[[file:figs/ty_relative_time.png]]
#+begin_src matlab
figure;
hold on;
plot(ty_1h(:, 3), lsim(1/s, ty_1h(:, 2)-ty_1h(:, 1), ty_1h(:, 3)), 'DisplayName', 'Relative Displacement- Ty - 1Hz');
plot(ty_on(:, 3), lsim(1/s, ty_on(:, 2)-ty_on(:, 1), ty_on(:, 3)), 'DisplayName', 'Relative Displacement- Ty - ON');
plot(ty_of(:, 3), lsim(1/s, ty_of(:, 2)-ty_of(:, 1), ty_of(:, 3)), 'DisplayName', 'Relative Displacement- Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Displacement [m]');
xlim([0, 2]);
legend('Location', 'southwest');
#+end_src
#+NAME: fig:ty_relative_disp_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_relative_disp_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_relative_disp_time
#+CAPTION: Relative Displacement of the sample with respect to the marble
#+RESULTS: fig:ty_relative_disp_time
[[file:figs/ty_relative_disp_time.png]]
** Frequency Domain
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
dt = ty_of(2, 3)-ty_of(1, 3);
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
#+end_src
Then we compute the Power Spectral Density using =pwelch= function.
First for the geophone located on the marble
#+begin_src matlab
[pxof_m, f] = pwelch(ty_of(:, 1), win, [], [], Fs);
[pxon_m, ~] = pwelch(ty_on(:, 1), win, [], [], Fs);
[px1h_m, ~] = pwelch(ty_1h(:, 1), win, [], [], Fs);
#+end_src
And for the geophone located at the sample position.
#+begin_src matlab
[pxof_s, f] = pwelch(ty_of(:, 2), win, [], [], Fs);
[pxon_s, ~] = pwelch(ty_on(:, 2), win, [], [], Fs);
[px1h_s, ~] = pwelch(ty_1h(:, 2), win, [], [], Fs);
#+end_src
Finally, for the relative velocity.
#+begin_src matlab
[pxof_r, f] = pwelch(ty_of(:, 2)-ty_of(:, 1), win, [], [], Fs);
[pxon_r, ~] = pwelch(ty_on(:, 2)-ty_on(:, 1), win, [], [], Fs);
[px1h_r, ~] = pwelch(ty_1h(:, 2)-ty_1h(:, 1), win, [], [], Fs);
#+end_src
And we plot the ASD of the measured velocities:
- figure [[fig:psd_marble_compare]] for the geophone located on the marble
- figure [[fig:psd_sample_compare]] for the geophone at the sample position
- figure [[fig:psd_relative_compare]] for the relative velocity
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px1h_m), 'DisplayName', 'Marble - Ty 1Hz');
plot(f, sqrt(pxon_m), 'DisplayName', 'Marble - Ty ON');
plot(f, sqrt(pxof_m), 'DisplayName', 'Marble - Ty OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([1, 500]);
#+end_src
#+NAME: fig:psd_marble_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_marble_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_marble_compare
#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone on the marble
#+RESULTS: fig:psd_marble_compare
[[file:figs/psd_marble_compare.png]]
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px1h_s), 'DisplayName', 'Sample - Ty 1Hz');
plot(f, sqrt(pxon_s), 'DisplayName', 'Sample - Ty ON');
plot(f, sqrt(pxof_s), 'DisplayName', 'Sample - Ty OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([1, 500]);
#+end_src
#+NAME: fig:psd_sample_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_sample_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_sample_compare
#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone at the sample location
#+RESULTS: fig:psd_sample_compare
[[file:figs/psd_sample_compare.png]]
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px1h_r), 'DisplayName', 'Relative - Ty 1Hz');
plot(f, sqrt(pxon_r), 'DisplayName', 'Relative - Ty ON');
plot(f, sqrt(pxof_r), 'DisplayName', 'Relative - Ty OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([1, 500]);
#+end_src
#+NAME: fig:psd_relative_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_relative_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_relative_compare
#+CAPTION: Comparison of the ASD of the relative velocity
#+RESULTS: fig:psd_relative_compare
[[file:figs/psd_relative_compare.png]]
** Ty motion and current
The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
*** Data pre-processing
Let's look at at the start of the csv file.
#+begin_src bash :results output
sed -n 1,30p mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
#+end_src
#+RESULTS:
#+begin_example
1 Elmo txt chart ver 2.0
2
3 [File Properties]
4 Creation Time,2019-05-13 05:33:43
5 Last Updated,2019-05-13 05:33:43
6 Resolution,0.001
7 Sampling Time,5E-05
8 Recording Time,5.461
9
10 [Chart Properties]
11 No.,Name,X Linear,X No.
12 1,Chart #1,True,0
13 2,Chart #2,True,0
14
15 [Chart Data]
16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
20
21 [Signal Names]
22 1,Time (sec)
23 2,Position [cnt]
24 3,Current Command [A]
25 4,Total Current Command [A]
26
27 [Signals Data Group 1]
28 1,2,3,4,
29 0,-141044,-0.537239575086517,-0.537239575086517,
30 0.001,-143127,-0.530803752974691,-0.530803752974691,
#+end_example
The real data starts at line 29.
We then load this =cvs= file starting at line 29.
#+begin_src matlab
tye_on = csvread("mat/Ty-when-Rz-1Hz.csv", 29, 0);
tye_1h = csvread("mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv", 29, 0);
#+end_src
*** Time domain data
We plot the position of the translation stage measured by the encoders.
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
The result is shown on figure [[fig:ty_position_time]].
#+begin_src matlab
figure;
subplot(1, 2, 1);
plot(tye_on(:, 1), (tye_on(:, 2)-mean(tye_on(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(tye_1h(:, 1), (tye_1h(:, 2)-mean(tye_1h(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');
#+end_src
#+NAME: fig:ty_position_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_position_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_position_time
#+CAPTION: Y position of the translation stage measured by the encoders
#+RESULTS: fig:ty_position_time
[[file:figs/ty_position_time.png]]
We also plot the current as function of the time on figure [[fig:ty_current_time]].
#+begin_src matlab
figure;
subplot(1, 2, 1);
plot(tye_on(:, 1), tye_on(:, 3)-mean(tye_on(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(tye_1h(:, 1), tye_1h(:, 3)-mean(tye_1h(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');
#+end_src
#+NAME: fig:ty_current_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_current_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_current_time
#+CAPTION: Current going through the actuator of the translation stage
#+RESULTS: fig:ty_current_time
[[file:figs/ty_current_time.png]]
** Conclusion
#+begin_important
-
#+end_important

250
disturbance-ty-sr/matlab/disturbance_ty_sr.m Normal file
View File

@@ -0,0 +1,250 @@
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
% Load data
ty_of = load('mat/data_050.mat', 'data'); ty_of = ty_of.data;
ty_on = load('mat/data_051.mat', 'data'); ty_on = ty_on.data;
ty_1h = load('mat/data_052.mat', 'data'); ty_1h = ty_1h.data;
% Voltage to Velocity
% We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
gain = 40; % [dB]
ty_of(:, 1) = voltageToVelocityL22(ty_of(:, 1), ty_of(:, 3), gain);
ty_on(:, 1) = voltageToVelocityL22(ty_on(:, 1), ty_on(:, 3), gain);
ty_1h(:, 1) = voltageToVelocityL22(ty_1h(:, 1), ty_1h(:, 3), gain);
ty_of(:, 2) = voltageToVelocityL22(ty_of(:, 2), ty_of(:, 3), gain);
ty_on(:, 2) = voltageToVelocityL22(ty_on(:, 2), ty_on(:, 3), gain);
ty_1h(:, 2) = voltageToVelocityL22(ty_1h(:, 2), ty_1h(:, 3), gain);
% Time domain plots
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 1), 'DisplayName', 'Marble - Ty 1Hz');
plot(ty_on(:, 3), ty_on(:, 1), 'DisplayName', 'Marble - Ty ON');
plot(ty_of(:, 3), ty_of(:, 1), 'DisplayName', 'Marble - Ty OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]);
legend('Location', 'southwest');
% #+NAME: fig:ty_marble_time_zoom
% #+CAPTION: caption
% #+RESULTS: fig:ty_marble_time_zoom
% [[file:figs/ty_marble_time_zoom.png]]
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2), 'DisplayName', 'Sample - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2), 'DisplayName', 'Sample - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2), 'DisplayName', 'Sample - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]);
legend('Location', 'southwest');
% Relative Velocity
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2)-ty_1h(:, 1), 'DisplayName', 'Relative Velocity - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2)-ty_on(:, 1), 'DisplayName', 'Relative Velocity - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2)-ty_of(:, 1), 'DisplayName', 'Relative Velocity - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]);
legend('Location', 'southwest');
% Frequency Domain
% We first compute some parameters that will be used for the PSD computation.
dt = ty_of(2, 3)-ty_of(1, 3);
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
% Then we compute the Power Spectral Density using =pwelch= function.
% First for the geophone located on the marble
[pxof_m, f] = pwelch(ty_of(:, 1), win, [], [], Fs);
[pxon_m, ~] = pwelch(ty_on(:, 1), win, [], [], Fs);
[px1h_m, ~] = pwelch(ty_1h(:, 1), win, [], [], Fs);
% And for the geophone located at the sample position.
[pxof_s, f] = pwelch(ty_of(:, 2), win, [], [], Fs);
[pxon_s, ~] = pwelch(ty_on(:, 2), win, [], [], Fs);
[px1h_s, ~] = pwelch(ty_1h(:, 2), win, [], [], Fs);
% Finally, for the relative velocity.
[pxof_r, f] = pwelch(ty_of(:, 2)-ty_of(:, 1), win, [], [], Fs);
[pxon_r, ~] = pwelch(ty_on(:, 2)-ty_on(:, 1), win, [], [], Fs);
[px1h_r, ~] = pwelch(ty_1h(:, 2)-ty_1h(:, 1), win, [], [], Fs);
% And we plot the ASD of the measured velocities:
% - figure [[fig:psd_marble_compare]] for the geophone located on the marble
% - figure [[fig:psd_sample_compare]] for the geophone at the sample position
% - figure [[fig:psd_relative_compare]] for the relative velocity
figure;
hold on;
plot(f, sqrt(px1h_m), 'DisplayName', 'Marble - Ty 1Hz');
plot(f, sqrt(pxon_m), 'DisplayName', 'Marble - Ty ON');
plot(f, sqrt(pxof_m), 'DisplayName', 'Marble - Ty OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([1, 500]);
% #+NAME: fig:psd_marble_compare
% #+CAPTION: Comparison of the ASD of the measured velocities from the Geophone on the marble
% #+RESULTS: fig:psd_marble_compare
% [[file:figs/psd_marble_compare.png]]
figure;
hold on;
plot(f, sqrt(px1h_s), 'DisplayName', 'Sample - Ty 1Hz');
plot(f, sqrt(pxon_s), 'DisplayName', 'Sample - Ty ON');
plot(f, sqrt(pxof_s), 'DisplayName', 'Sample - Ty OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
% #+NAME: fig:psd_sample_compare
% #+CAPTION: Comparison of the ASD of the measured velocities from the Geophone at the sample location
% #+RESULTS: fig:psd_sample_compare
% [[file:figs/psd_sample_compare.png]]
figure;
hold on;
plot(f, sqrt(px1h_r), 'DisplayName', 'Relative - Ty 1Hz');
plot(f, sqrt(pxon_r), 'DisplayName', 'Relative - Ty ON');
plot(f, sqrt(pxof_r), 'DisplayName', 'Relative - Ty OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
% #+RESULTS:
% #+begin_example
% 1 Elmo txt chart ver 2.0
% 2
% 3 [File Properties]
% 4 Creation Time,2019-05-13 05:33:43
% 5 Last Updated,2019-05-13 05:33:43
% 6 Resolution,0.001
% 7 Sampling Time,5E-05
% 8 Recording Time,5.461
% 9
% 10 [Chart Properties]
% 11 No.,Name,X Linear,X No.
% 12 1,Chart #1,True,0
% 13 2,Chart #2,True,0
% 14
% 15 [Chart Data]
% 16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
% 17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
% 18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
% 19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
% 20
% 21 [Signal Names]
% 22 1,Time (sec)
% 23 2,Position [cnt]
% 24 3,Current Command [A]
% 25 4,Total Current Command [A]
% 26
% 27 [Signals Data Group 1]
% 28 1,2,3,4,
% 29 0,-141044,-0.537239575086517,-0.537239575086517,
% 30 0.001,-143127,-0.530803752974691,-0.530803752974691,
% #+end_example
% The real data starts at line 29.
% We then load this =cvs= file starting at line 29.
ty_on = csvread("mat/Ty-when-Rz-1Hz.csv", 29, 0);
ty_1h = csvread("mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv", 29, 0);
% Time domain data
% We plot the position of the translation stage measured by the encoders.
% There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
% The result is shown on figure [[fig:ty_position_time]].
figure;
subplot(1, 2, 1);
plot(ty_on(:, 1), (ty_on(:, 2)-mean(ty_on(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(ty_1h(:, 1), (ty_1h(:, 2)-mean(ty_1h(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');
% #+NAME: fig:ty_position_time
% #+CAPTION: Y position of the translation stage measured by the encoders
% #+RESULTS: fig:ty_position_time
% [[file:figs/ty_position_time.png]]
% We also plot the current as function of the time on figure [[fig:ty_current_time]].
figure;
subplot(1, 2, 1);
plot(ty_on(:, 1), ty_on(:, 3)-mean(ty_on(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(ty_1h(:, 1), ty_1h(:, 3)-mean(ty_1h(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');